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WITH THE COMPLIMENTS 
OF THE AUTHOR 



A TALK ON TEACHING 

Given at a Conference of Members of the Instructing Staff of 
the Massachusetts Institute of Technology 



By ARTHUR A. NOYES 






10 1 1 



A TALK ON TEACHING 

Given at a Conference of Members of the Instruct- 
ing Staff of the Massachusetts Institute of 
Technology on March 20, 1908* 

by arthur a. noyes 

In speaking to you to-day upon the subject of teaching, 
I shall try to present some considerations, suggested by 
my own experience, in regard to the application of edu- 
cational principles to our own problems. Much of what 
I shall say will doubtless be familiar to a body of teachers 
like yourselves. Yet it is perhaps desirable that even the 
commonplaces of education be brought before us from 
time to time; for, though we recognize the abstract prin- 
ciples that should be followed, yet it is only by constant atten- 
tion to them that we shall succeed in making them the real 
foundation of our courses of instruction. 

Throughout our considerations we must keep in view 
the aim of the education for which the Institute stands. In 
regard to this there is, I believe, little difference of opinion. 
The aim is to produce men who have the power to solve 
the industrial, engineering, and scientific problems of the 
day, — men who shall originate and not merely execute. 
The fundamental question is then. How shall we develop 
this power ? It is power that counts, and not knowledge. 
The ultimate test is what a man can do, not what he knows; 
and this is the test we should apply to our students upon 
the completion of each subject of instruction, and to our 
graduates at the close of their period of study at the Institute. 

* To Professor H. G. Pearson I desire to express my great indebtedness for his sugges- 
tions and assistance in connection with the preparation of this paper for the printer. 



It is true that a part of the power of a scientific man 
depends upon his knowledge; and a part of our task as 
teachers consists in bringing him into permanent possession 
of those kinds of knowledge which are most essential. In 
connection with this work of imparting knowledge I ask 
you to note three kinds of errors into which we are especially 
apt to fall. 

First, it is a common mistake to ply the student with 
more than he can possibly assimilate. For covering a cer- 
tain subject we are allowed a limited number of hours; 
into that time we feel that we must crowd at any rate all 
the obviously important topics. This we make the con- 
sideration of prime importance, whereas we should first 
determine what principles and essential facts can, in the 
amount of time given, be treated with sufficient thorough- 
ness to enable the student really to comprehend them and 
make them his own. We must therefore constantly exam- 
ine the courses that we are giving, to see whether they are 
not overcrowded; and, if they are overcrowded, we must 
consider how they may be disencumbered, so that the main 
points may be properly emphasized. Obiter dicta have no 
place in a course of instruction: principles which there is 
not time to drive home should not be mentioned at all; for 
they simply confuse the student, by distributing his atten- 
tion over a larger number of topics than he can possibly 
assimilate at one time. 

The existing conditions make the commission of this 
error only too easy. There is a constant demand that we 
give our students a wide variety of information. Not to 
teach a phase of a subject which may be regarded as impor- 
tant invites criticism and argues incapacity on the part of 
the teacher. Moreover, in many subjects we are badly off 
in the matter of text-books: most of our so-called text- 



books are really treatises and reference books. Would 
that some competent person would write for a ninety-hour 
course in chemistry or physics a text-book containing only 
those facts and principles that can be properly taught in 
a ninety-hour course! It is this defect which has led so many 
of the Institute professors to prepare notes of their own, 
the object of which is primarily to emphasize the more 
fundamental principles of the subject. 

Notwithstanding these difficulties, however, it is our 
clear duty as teachers constantly to endeavor not so much 
to teach many things as to teach well, — not so much to 
"cover the ground" ourselves, as to make sure that our 
students go over the course with us. In trying to include 
too much, we not only sacrifice the opportunity for train- 
ing, of which I shall speak later, but we accomplish far 
less than we might even in the matter of imparting 
knowledge. 

The second error of which I would speak is the failure 
to keep sufficiently in touch with the mind of the student — 
to appreciate the knowledge which he actually possesses 
and the degree of development of his mental powers. The 
unfortunate results of this error are most clearly and fre- 
quently observed in lecture courses. The lecturer is apt 
to look at his task merely from an objective view-point: 
if he presents his subject clearly and logically, he com- 
placently feels that he has done his part, and that it is the 
fault of the student if he has failed to profit by it. Yet the 
real test of the success of a lecture course, as of any other 
form of instruction, is the amount of benefit that the student 
actually derives from it; and the teacher must frequently, by 
some means or other, apply this test, must consider the 
causes of his incomplete success, and introduce such modi- 
fications as seem Hkely to lead to better results. He must 



keep in touch with the student so that he may appreciate 
his difficulties. This can be done much better in recitations 
than in lectures, but best of all through personal conferences; 
and, when conditions make it necessary to give lectures 
at all, they should be largely supplemented by these means, 
so that there may be individual contact with the student. 
It is to be hoped that the plan of regular conferences for 
which formal provision has already been made in first-year 
English and mathematics may be soon extended to other 
subjects; but in the mean time much is being done in this 
direction in an informal way by many of our best instructors. 
I wish only to emphasize the idea that such efforts are a 
well-paying investment of the teacher's time. They not only 
enable him to assist the individual student in a variety of 
ways, but they show the teacher the defects of his own 
methods of presentation and establish a cordial relationship 
between him and his class. 

One important cause of this imperfect adaptation to the 
mental needs of the student is the lack of correlation between 
the different subjects of instruction. A teacher ought to 
know both what the student has already learned in his 
previous courses and what he will need to know in the later 
dependent subjects. To this end it is important that instruc- 
tors should attend exercises in other subjects than their 
own, examine the text-books used, the notes and prob- 
lems given out, and the experiments performed. For ex- 
ample, every instructor teaching applied mathematical 
subjects in the higher years of the various Courses should 
famiHarize himself with the new plan of teaching mathe- 
matics which has been recently introduced. I believe, in a 
large school like the Institute, the imperfect correlation of the 
different subjects of instruction is one of the most serious 
evils, and one which must be met by an increased effort 



on the part of each instructor to know about the work that 
is being done in subjects related to his own. 

The third difficulty which I would refer to is that which 
arises from the tendency of the student to learn by mem- 
orizing and to do his work in the laboratory mechanically, 
without thinking. We must not allow ourselves merely 
to mourn over the fact that the average student won't think 
if he can help it, or try to justify our failures to get him to 
do so by reflections on his earher education. We must 
face the situation as it actually is, and realize that it is one 
of the most important parts of our problem to make the 
student think. 

Herbert Spencer is reported to have said, "if he read as 
much as other people, he would know as Httle as they." 
The remark is worth remembering, in spite of its compla- 
cency, for the light it throws on the worthlessness of what- 
ever is done without thinking. In science, as in other 
departments of knowledge, no acquisition is real and per- 
manent which is not won by hard thought. As every 
teacher knows, a most effective way of making a student 
think is by constant questioning. He emphasizes a prin- 
ciple by asking questions about its possible applications. 
He answers one question by asking another, and, if pos- 
sible, gets the student to put the questions for himself. 
The good teacher is constantly trying to lead the student 
on, but he refuses to carry him. In the laboratory and 
drawing-room, where students tend to work as if their whole 
purpose were to go through the mechanical operations as 
rapidly as possible, the successful instructor will be con- 
stantly on the alert to check this tendency. He will be 
with the student at his desk as much as possible, not telHng 
him what to do, but seeing that he understands and plans 
out his work for himself. Only in matters of manipulation 



and technique should a distinctly different plan of instruc- 
tion be adopted. Here, in order to economize time for 
more important work, the effort should be made to give 
the student the necessary manual skill as rapidly as possi- 
ble, by giving him detailed instruction and showing him 
by example the little artifices that make the expert manipu- 
lator. The engineer, architect, or chemist, must have a 
good technique, and we cannot afford to neglect it; but 
one of our problems is to reduce the time needed for its ac- 
quirement to its lowest limit. 

Summing up now this discussion of the question of impart- 
ing knowledge, I would advise especially: — 

1. That we take care not to include in our courses more 
than the average student can properly assimilate. 

2. That we keep in close touch with the actual knowl- 
edge and mental development of the student; that to this 
end we introduce recitations and invite individual confer- 
ences as far as possible; and that we inform ourselves more 
fully in regard to the work which is done in courses related 
to our own. 

3. That we discourage the habit of memorizing and of 
working in a thoughtless, mechanical way in the labora- 
tories and drawing-rooms by close personal contact with 
the student and by appropriate modifications of our courses 
and of the examinations upon them. 

I come now to the other more important and more diffi- 
cult task of giving the student the mental training upon 
which the power of handling new undertakings and solv- 
ing new problems depends. In comparison with this the 
imparting of knowledge is an insignificant matter. One 
of our professors has given an apt illustration of the true 
function of the Institute. It should be, he says, a gym- 
nasium where the faculties are exercised and developed, 



7 

and not a boarding-house where the students are crammed 
with facts. We want our young men to acquire the power 
of solving problems; and this, Hke any other faculty, can 
only be developed by constant exercise of it. Therefore, 
we must make problems one of the main features of our 
courses, — problems in the broadest sense, not merely nu- 
merical apphcations of principles. Class-room and draw- 
ing-room and laboratory work alike must consist largely 
in the solution of problems. 

This matter of problems seems to me of so much impor- 
tance that I would hke to consider it with you in some detail. 

First a few words as to the character of our problems. 
In the lower schools the questions given out for solution 
are well called "examples": that is, a teacher does a prob- 
lem in a certain way, as an example; and the students learn 
by imitation to do others like it. Of course, for our pur- 
poses this kind of problem-solving is of scarcely any value. 
We must avoid problems which are only pattern-work and 
those which are simply the substitution of numerical values 
in formulas. One of our professors who makes problems 
a large part of his course told me of the student who came 
to him with the complaint that he couldn't do his prob- 
lems because each one was different from the others, well 
showing the kind of problem-work to which he had been 
accustomed. 

There are two classes of problems that are essential to 
our work, — the kind that develop logical thinking or reason- 
ing power and the kind that develop imaginative thinking 
or the power of planning and originating. For each of these 
two kinds of problems we should try to make better provi- 
sion; but the latter kind needs, I beheve, special develop- 
ment at the Institute. For example, we ought to a greater 
extent require in our laboratories that the students plan 



out their own experiments. Students should be told what 
apparatus is available and what results are wanted, and then 
should be left largely to their own ingenuity to produce those 
results. In each particular line of study there is, more- 
over, a particular form of problem-work that is appropriate. 
In engineering subjects it is the design of new structures and 
of new machines; in the descriptive sciences it is the iden- 
tification of materials (provided this be done not by tables 
nor bjf a set method of procedure, but by the student himself 
upon the basis of his own knowledge); in English it is the 
writing of themes; and so on. Each teacher must consider 
how his subject can be presented so as to afford the largest 
opportunity for developing the student's reasoning power 
and creative ability. 

Permit me next to say a few words in regard to the im- 
portance of independent work in the solving of problems. 
I believe that only by insisting upon this can anything like 
the full benefit be secured. In the first place, what we 
want to do is not to teach the student how to solve certain 
particular problems, but to train him in original thinking, 
— to solve any kind of problem; and to this end he must 
do the work himself. Secondly, the line cannot be effec- 
tively drawn at any other point than that of absolute inde- 
pendence. If one allows working together at all, some 
students will copy, and a still greater number will get other 
students to do all the thinking for them. Then, again, if 
problems form a large part of the term's work, the marks 
of the term ought to be based principally upon those prob- 
lems; and this is not fair unless we are able to assure our- 
selves that the results represent individual work. When 
this requirement is made of the student, the instructor must 
be ready to assist him in his difficulties, and must provide 
definitely for opportunity for consultation; else the conscien- 



tious student will waste an undue amount of time before 
some obstacle which a few minutes' talk with the teacher 
would remove. It is, I think, very desirable to introduce 
more extensively the plan, already followed in some sub- 
jects, of requiring problems to be done at assigned hours 
under the guidance of the instructor rather than in outside 
hours of preparation. I am well aware that there are some 
advantages in allowing students of the same proficiency to 
work out their problems together: difficulties are gotten 
over with less loss of time, the principles involved become 
clearer by discussion, and the work is made more attractive. 
In exceptional cases, especially with small classes of rather 
advanced students, who have acquired the true point of 
view, these advantages may be secured without incurring 
the evils to which I have referred; but I believe that this 
is true only in such exceptional cases, and that the differ- 
ence in the emphasis laid upon independent work by 
different instructors is a source of demoralization to our 
students. 

The introduction of more problem work naturally carries 
with it the laying of greater weight on the term work and 
less on the final examination in determining the record of 
the student, — a thing which is in itself highly desirable. An 
instructor is sometimes heard to say, "If a man gets the 
subject in the end, it is all right." That remark shows, 
I think, that he does not have the true conception of the main 
purpose of his course, which is not to give a certain amount 
of knowledge in the subject, but to give a mental training 
which can only be acquired gradually by persistent effort 
through the whole term. Indeed, in my own opinion, one 
of the most effective means of raising the standard of our 
instruction is the abandonment of final examinations in 
more of our courses. Thereby not only are the many serious 



lO 



evils of the examination system removed, — such as the post- 
ponement of serious study till the end of the term, the cram- 
ming during a short period before the examinations (which 
is, I believe, wrongly regarded by some instructors who do 
not appreciate the character of cramming methods as valu- 
able in affording a review and perspective of the whole 
subject), the attendant nervous strain and injury to health, 
the evils of tutoring and proctoring, — but also because it 
impresses upon both instructor and student a different edu- 
cational ideal, that of training the mind rather than storing 
it with knowledge. Some years ago the faculty took the 
step of abolishing final examinations in many first and 
second year subjects. I think the time has come when pro- 
vision should be made b)^ individual instructors and by the 
faculty for the extension of this plan to many other subjects. 

These considerations may be summed up by saying that 
problem- solving is by far the most effective means we have 
of developing mental power. We must make such work 
as large as possible a part of our courses, making place for 
it by the omission of much other material, important though 
it may be. We must insist on independent work in the 
solution of problems, but in doing it we must be ready to 
give assistance to the individual student. Our examina- 
tions should be made a test of his power to handle problems 
connected with the subject rather than a test of his knowl- 
edge; and the record we give him should depend mainly 
on his success in this direction. 

Let me pause here to make one remark, lest I should seem 
to underestimate the success which is already being attained 
by the teachers of the Institute. Any one famihar with 
our work well knows that what I have said in regard to 
the relative importance of knowledge and training and the 
methods of developing mental power is only an expression 



II 



of the general educational policy of the Institute, and that 
the principles I have discussed have already been exten- 
sively put into practice here, — probably to a greater extent 
than in any other large educational institution. I have 
emphasized these principles only in the hope of impressing 
each individual instructor more fully with their importance 
and of encouraging him to aim to base his own teaching 
upon them as largely as possible. 

So far I have considered only that side of our work which 
relates to the professional training of the engineer or the 
scientist; but, as we all know, the problem of the Insti- 
tute is not confined to this. It is our function to give a 
general education in combination with a professional train- 
ing, — to educate the man as well as the engineer. We must 
constantly bear in mind this twofold aspect of our work, 
and must be contented to sacrifice in some measure pro- 
fessional attainment in the interest of a broader education. 
We must aim to develop those qualities which are the result 
of a liberal training,— breadth of view, perspective, and 
soundness of judgment; but we must especially aim to 
develop character and high ideals. The acquirement of 
power is, as I have said, the intellectual goal towards which 
we are striving; but we must also keep in view the moral 
end, which is the cultivation of the spirit which will lead 
that power to be devoted to some high form of service. 

Some may perhaps contend that these are not our func- 
tions, — that our obligations are only on the intellectual 
side, that the development of the moral, social, aesthetic, 
and physical quahties of the student are to be left to out- 
side influences. Such a view is, in my judgment, a seriously 
mistaken one. It might well be held by the authorities 
of a graduate school of the purely professional type; but 
it is quite inconsistent with the conception of the Institute 



12 



as an undergraduate school, whose primary function is to 
furnish an effective form of general education. Our stu- 
dents come to us during four years of the most critical 
period of life, when their habits of thought and ideals of life 
are being formed; and we must appreciate the seriousness 
of the trust which is thereby imposed upon us. It is of 
comparatively little significance whether the student acquires 
more or less knowledge of mathematics, chemistry, physics, 
or engineering; but it is vitally important that his mental 
power, his general culture, his character, and his ideals be 
adequately developed. We must therefore take care not 
to interpret our function as teachers too narrowly; but we 
must each of us improve every opportunity for contributing 
to the more general and more important result which the 
Institute has in view. The means for attaining this result 
certainly deserve especial consideration in a talk on teach- 
ing. I have already expressed my ideas at some length 
on the development of mental power. Owing to the limited 
time remaining, I shall not attempt to discuss the means 
of developing those important qualities which are summed up 
in the word "culture"; but I should like to consider with you 
briefly the still more vital question of what can be done to 
develop character and high ideals. The indefiniteness of 
the methods by which this may be accomplished makes 
the subject a particularly difficult one; but it must not be 
passed over on this account. 

The methods of the Institute are especially adapted to 
develop those habits which go to the formation of character. 
To meet the demands of our curriculum, the student must 
be willing to subordinate pleasure to duty; he must work 
industriously and persistently; he must, too, work rapidly, 
whereby he comes to appreciate the value of time. Our 
scientific courses offer, moreover, special opportunities 



13 

for inculcating habits of accuracy, reliability, clearness of 
expression, neatness, and orderliness; and we must insist 
that the work be so carried out that these benefits do in fact 
result. Careless or slovenly work of any kind must be 
vigorously condemned. We should see that note-books 
be kept in a neat and orderly manner; that reports be 
written clearly in good literary form; that in the class- 
room accuracy of expression be cultivated; that the numer- 
ical work connected with problems be accurately performed 
(nothing hke full credit being given when merely "the 
principle is correct"); and that every reasonable effort 
be made to verify an experimental result or confirm a con- 
clusion before it is accepted as final. The teacher of any 
science who says it is not his business to attend to these 
things does not, in my opinion, understand his business, 
which is not so much to teach the subject-matter of the 
science as it is to teach scientific method and to cultivate 
the scientific spirit. 

Yet the formation of character, important as it is, is by 
no means the whole of this side of our task. The quahties 
that make up a good character in the narrower sense are, 
after all, only "the half-virtues which the world calls best." 
That the man may be really effective, these must be sup- 
plemented by high ideals of service, a strong purpose in 
life, and a real devotion to it. With respect to means 
of imparting such ideals, I have only a few thoughts to 
present. 

In the first place, I believe that, to accomplish much in 
this direction, we must get into personal relations with the 
student. Thereby many different opportunities of influ- 
encing him are opened to us. To begin with, we set him 
the example of rendering unselfish service to others by 
giving him individual aid beyond that which our formal 



obligations in class-room and laboratory •demand. Let us 
make it clear to him that it is not our primary purpose to 
"maintain the standard," but that we are personally inter- 
ested in aiding him to fulfil the established requirements. 
Up to the end of the course the teacher should consider 
every student who is doing unsatisfactory work as one of 
the problems for which he must try to find a solution; and 
there is, I believe, no better way of securing attention from 
a student who is neglecting his work or of bringing up to the 
standard one who is having difficulty with the subject than 
by showing a personal interest in him. I know that this 
makes an added demand on the instructor, and that what 
any one can do in this way is limited; yet it is an aim to be 
kept in mind and to be striven for. Since at the Institute 
there is one instructor to about seven students, the net 
result would be very large if each teacher would endeavor 
to become well acquainted with even this number of his 
students. 

Close contact enables the teacher, too, to influence in a 
pronounced way the point of view of the student, both with 
reference to his work at the Institute and to his ultimate 
aims. On occasions when I have talked intimately with 
students about these matters, I have often felt keenly how 
much more they need advice about Itfe than about chem- 
istry. Such individual conversations furnish also the oppor- 
tunity of giving the student a broader interest by letting him 
know of the scientific and professional problems in which 
ourselves and others are engaged. He thus sees more clearly 
the future before him, and appreciates better the value of 
the studies he is pursuing. 

Though personal contact is by far the most effective 
way of exerting these general influences, yet, since it is pos- 
sible to provide for it only to a limited extent, we must 



IS 

improve the opportunities which our regular courses of 
instruction afford for securing the desired result. 

Some of the ways in which this may be accompHshed 
are to indicate the wide scope of scientific generaHzations 
and the beauty of theoretical explanations, to point out 
the important technical applications of the principles pre- 
sented, to describe the considerations and experiments 
which led to their discovery and the participation of indi- 
vidual scientists in their development, and to indicate some 
of the numerous problems of the science that still await 
solution. By thus emphasizing the broad scientific as- 
pects, the practical bearing, and the historical and bio- 
graphical development of our existing knowledge, and by 
impressing the student with the idea that at present "our 
science is a drop, our ignorance a sea," we may do much 
to awaken his interest in knowledge for its own sake and to 
develop in him broader points of view and higher aims. 
Especially must the importance of these considerations be 
borne in mind in subjects that have to be presented by for- 
mal lectures. I have already indicated my opinion that 
as a means of imparting a fundamental knowledge and of 
giving a mental training the lecture plan is strikingly ineffec- 
tive, and can be justified from these points of view only on 
grounds of economy. It does, however, have in non-techni- 
cal subjects what may be called a cultural function of some 
importance; for it provides, better than the recitation 
plan, the opportunity of arousing the broader interests of 
which I have been speaking. 

In conclusion, as a summing up of these considerations, 
I would urge that we take care not to interpret our work 
as teachers too literally, — that we realize that our task is a 
much larger one than that of imparting a knowledge of our 
particular subject, and that it is a broader one even than 



that of developing the power of dealing with its problems; 
that, in fact, the most important and most difficult part of 
our undertaking consist in cultivating sound habits of thought 
and work, in developing breadth of interest and good judg- 
ment, in moulding character, and in creating a high moral 
purpose. 



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